Thermodynamic Characteristics of a Spherical Molecular Surfactant Aggregate in a Quasi-Droplet Model

The model of spherical molecular aggregate of nonionic surfactant is proposed. This model allows for the maximal (in accordance with packing rules) penetration of water molecules into an aggregate and is an alternative to the droplet model of molecular aggregate. Necessary conditions for the applicability of a model named quasi-droplet model are formulated. Based on this model, the dependence of the work of molecular aggregate formation on the aggregation number and surfactant monomer concentration in solution that plays the key role for the theory of micellization is studied. The equation is derived for the coordinates of maximum and minimum of aggregate formation work on the aggregation number axis arising with an increase in the concentration of micellar solution. Model calculations of the thermodynamic characteristics of the kinetics of micellization are performed. The approximation of the work of molecular aggregate formation allowing for the analytical study is constructed.     

Characterization of micelle formation of dodecyldimethyl-N-2-phenoxyethylammonium bromide in aqueous solution

Aggregation behavior of dodecyldimethyl-N-2-phenoxyethylammonium bromide commonly called domiphen bromide (DB) was studied in aqueous solution. The Krafft temperature of the surfactant was measured. The surfactant has been shown to form micellar structures in a wide concentration range. The critical micelle concentration was determined by surface tension, conductivity, and fluorescence methods. The conductivity data were also employed to determine the degree of surfactant counterion dissociation. The changes in Gibb's free energy, enthalpy, and entropy of the micellization process were determined at different temperature. The steady-state fluorescence quenching measurements with pyrene and N-phenyl-1-naphthylamine as fluorescence probes were performed to obtain micellar aggregation number. The results were compared with those of dodecyltrimethylammonium bromide (DTAB) surfactant. The micelle formation is energetically more favored in DB compared to that in DTAB. The 1H-NMR spectra were used to show that the 2-phenoxyethyl group, which folds back onto the micellar surface facilitates aggregate formation in DB.     

Boltzmann distributions and slow relaxation in systems with spherical and cylindrical micelles

Equilibrium and nonequilibrium distributions of molecular aggregates in a solution of a nonionic surfactant are investigated at the total surfactant concentration above the second critical micelle concentration (CMC2). The investigation is not limited by the choice of a specific micellar model. Expressions for the direct and reverse fluxes of molecular aggregates over the potential humps of the aggregation work are derived. These aggregation work humps set up activation barriers for the formation of spherical and cylindrical micelles. With the aid of the expressions for molecular aggregate fluxes, a set of two kinetic equations of micellization is derived. This set, along with the material balance equation, describes the molecular mechanism of the slow relaxation of micellar solution above the CMC2. A realistic situation has been analyzed when the CMC2 exceeds the first critical micelle concentration, CMC1, by an order of magnitude, and the total surfactant concentration varies within the range lying markedly above the CMC2 but not by more than 2 orders of magnitude. For such conditions, an equation relating the parameters of the aggregation work of a cylindrical micelle to the observable ratio of the total surfactant concentration and the monomer concentration is found for an equilibrium solution. For the same conditions, but in the nonequilibrium state of materially isolated surfactant solution, a closed set of linearized relaxation equations for total concentrations of spherical and cylindrical micelles is derived. These equations determine the time development of two modes of slow relaxation in micellar solutions markedly above the CMC2. Solving the set of equations yields two rates and two times of slow relaxation.     

Thermodynamic and Kinetic Foundations of the Micellization Theory: 5. Hierarchy of Kinetic Times

The characteristic kinetic times of micellization in the solution of a nonionic surfactant: the times of establishment of quasi-equilibrium concentrations of molecular aggregates in micellar, subcritical, and overcritical regions, times of establishment of quasi-equilibrium concentrations of molecular aggregates in the near-critical region of their sizes, the average time between two successive acts of emission of surfactant monomers by a micelle, the average value of micelle lifetime, the time of establishment of quasi-stationary mode of matter exchange between the solution and molecular aggregate, as well as the times of fast and slow relaxation in a solution were analyzed. The hierarchy of these times disclosing complex multistage kinetic process of micelle formation and decomposition and the establishment of equilibrium in the micellar solution was revealed. It was shown that this hierarchy is provided by the small parameters of the kinetic theory. The inverse problem of micellization kinetics was discussed; this problem allows us to find the characteristics of the formation work for micellar aggregate from the experimental data on the relaxation time of micellar solution.     

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.     

Nanostructural Models of Micelles and Primicellar Aggregates

For the case of direct spherical micelles, two nanostructural models of molecular aggregates have been discussed: the classical drop model implying flexibility of hydrocarbon chains of molecules and their full immersion into the hydrocarbon core of an aggregate, and a quasi-drop model allowing partial outcropping of the chains in the strainless state from the core. For the sake of simplicity, a solution is assumed to contain only a single surfactant whose molecules possess only one, unbranched hydrocarbon radical. Within the frames of the models, the behavior of the chemical potential of surfactant molecules in a primicellar and micellar molecular aggregate has been analyzed, as well as the work of formation of the molecular aggregate as a function of the aggregation number and the solution concentration.     

The mass action law theory of micellar solutions

Theories of micellization based on the application of the mass action law to aggregation processes in surfactant solutions are reviewed. The rigorous thermodynamic justification of the approach, explanation of the critical micelle concentration, inter-relations between the main micellization parameters, and an analysis of the surface tension isotherm of a micellar solution are given. Properties of ionic micellar systems, including counterion binding and the behavior of free monomeric ions, are discussed in detail with illustrative estimations for sodium dodecylsulfate and other surfactants.     

Micelle formation of N-(1,1-dihydroperfluorooctyl)- and N-(1,1-dihydroperfluorononyl)-N,N,N-trimethylammonium chlorides

Micelle formation of N-(1,1-dihydroperfluorooctyl)-N,N,N- and N-(1,1-dihydroperfluorononyl)-N,N,N-trimethylammonium chloride was investigated by analyzing the concentration dependence of the electric conductivity and of the activity of the counterion (Cl(-)) of the solution. The three micellization parameters for ionic surfactants, the micellization constant K(n), the micelle aggregation number n, and the number of counterions per micelle m, were determined by combination of electric conductivity and counterion concentration. The present analysis employed two slopes of the plots of specific conductivity against surfactant concentration below and above the critical micelle concentration and the mass action model of micelle formation. The aggregation numbers thus obtained were relatively small, while the degrees of counterion binding to the micelle (m/n) were found to be quite large, much larger than expected from the small aggregation numbers. Thermodynamical parameters of the micellization were evaluated from the temperature dependence of the three parameters, and the micellization of the fluorinated surfactant was found to be enthalpy-driven. A CF(2) group in the perfluorocarbon chain was found to be 1.44 times larger in hydrophobicity for micellization than a CH(2) group in the hydrocarbon chain.     

链式与面式两种不对称疏水结构表面活性剂之间的相互作用热力学

本文通过等温滴定量热法(ITC)、电导法和浊度法研究了阴离子生物表面活性剂脱氧胆酸钠(NaDC)及其与相反电荷的十二烷基三甲基溴化铵(DTAB)在水溶液中的自组装热力学.ITC结果支持了NaDC在水溶液中先生成预胶束再形成稳定胶束的分步聚集模型,由此得到了NaDC的预胶束和胶束化过程的一系列热力学参数,并讨论了它们形成的热力学机理.进一步研究了具有头-尾链式和疏水-亲水刚性面式非对称结构的DTAB/NaDC混合体系的聚集热力学行为,得到了富NaDC临界混合胶束浓度(cmcmix)、富DTAB临界胶束浓度(CM)及对应过程的转变焓.结果表明,NaDC面式结构与DTAB链式结构的对称性差异以及相反电荷的相互作用,导致混合体系有别于单一表面活性剂或头-尾链式结构的混合体系的聚集行为.混合溶液的聚集行为受控于表面活性剂浓度和摩尔分数的变化.富NaDC胶束化过程为熵驱动,而富DTAB的两种胶束形态转变过程为熵焓共同驱动的热力学机理.这些结果对于从热力学角度认识胆汁酸盐的自组装机理以及与传统的头-尾链式结构的表面活性剂相互作用机理和相行为有重要的意义.     

Mass action model for solute distribution between water and micelles. Partial molar volumes of butanol and pentanol in dodecyl surfactant solutions

The densities of 1-butanol and 1-pentanol were measured in aqueous solutions of dodecyltrimethylammonium bromide and dodecyldimethylamine oxide and the partial molar volumes at infinite dilution of the alcohols in aqueous surfactants solutions were obtained. The observed trends of this quantity as a function of the surfactant concentration were rationalized using a mass-action model for the alcohol distribution between the aqueous and the micellar phase. At the same time, the model was revised to account for the alcohol effect on the surfactant micellization equilibrium. The partial molar volume of alcohols in the aqueous and in the micellar phases and the ratios between the binding constant and the aggregation number were calculated. These thermodynamic quantities are nearly the same in the two surfactants analyzed in this paper but differ appreciably from those in sodium dodecylsulfate. The apparent molar volume of surfactants in some hydroalcoholic solutions at fixed alcohol concentration were also calculated. In the micellization region the trend of this quantity as a function of the surfactant concentration shows a hump, which depends on the alcohol concentration and on the alcohol alkyl chain length. The alcohol extraction from the aqueous to the micellar phase due to the addition of the surfactant can account for the observed trends.     

Relations for extrema of the work of aggregation in micellar solutions

Exact relations for the dependence of the positions of extrema of the aggregation work on the aggregation number axis on the surfactant monomer concentration are found for a dilute micellar solution. Relations for the half-widths of the vicinities of the extrema of the aggregation work are determined also. These half-widths are determined by the condition that, within the boundaries of their values, the aggregation work deviates from its extreme values by a thermal unit. The relations derived are illustrated by calculations based on the droplet and quasi-droplet models of spherical aggregates of nonionic surfactant. Some important applications of the obtained results to the theory of relaxation in micellar solutions are considered.     

Toward a Theory of Diffusion of a Nonionic Surfactant with Variable Aggregation Number in a Micellar System

Since the aggregation number of micelles always grows with concentration, and, in some cases this dependence is noticeable even for spherical micelles, there is a need to revise the theory of micellization, in which the aggregation number is assumed to be constant. This work reformulates the theory of diffusion of nonionic surfactants in micellar solutions with regard to the variability of the aggregation number. A new formula, which expresses the diffusion coefficient of a surfactant via the diffusion coefficients of monomers and micelles, contains an additional factor capable of increasing the diffusion coefficient with the surfactant concentration. However, this factor is not overly strong, and the “old” part of the formula acts in the opposite direction; as a result, the conventional decrease in the diffusion coefficient of a nonionic surfactant remains prevailing. The analytical consideration has been supplemented with numerical calculations, the results of which are presented in the tables.     

Conductometric and spectrofluorimetric characterization of the mixed micelles constituted by dodecyltrimethylammonium bromide and a tricyclic antidepressant drug in aqueous solution

Conductivity and static fluorescence measurements have been carried out at 25 degrees C to study the monomeric and micellar phases of aqueous solutions of mixed micelles constituted by a conventional cationic surfactant, dodecyltrimethylammonium bromide (D(12)TAB), and a tricyclic antidepressant drug, amitriptyline hydrochloride (AMYTP), with aggregation properties. From conductivity data, the total mixed critical micelle concentration and the dissociation degree of the mixed micelle have been obtained, while fluorescence experiments allow for the determination of the total aggregation number, and the micropolarity of micellar inside. Furthermore, the partial contribution of each surfactant to the mixed micellization process, through their critical micelle concentrations and their aggregation numbers have been determined, as well. The solubilization of the drug in the mixed micelles has been also studied through the mass action model, by determining the association constant between the micelles and the drug. From these results, the use of the micelles studied in this work as potential models for vectors of antidepressant drugs of the amitriptyline family has been discussed. The theoretical aspects of the mixed micellization process have been also analyzed.     

Self-assembly of tetradecyltrimethylammonium bromide in glycerol aqueous mixtures: A thermodynamic and structural study

In this paper, we have studied the effect of glycerol on the micelle formation of tetradecyltrimethylammonium bromide. Changes in both the critical micelle concentration and the degree of counterion binding of the surfactant upon the addition of glycerol across a temperature range (20-40 degrees C) were examined by using the conductance method. The equilibrium model of micelle formation was applied to obtain the thermodynamic parameters of micellization. An enthalpy-entropy compensation effect was observed in all the solvent systems, but whereas the micellization of the surfactant in the medium with 20% glycerol occurs under the same structural conditions as in pure water, in glycerol rich mixtures the results suggest that the lower aggregation in these media is due to the minor cohesive energy of the solvent system in relation to water. It was also observed that the micellar aggregation number, as obtained by the static quenching method, decreases with the glycerol content. This fact was attributed to an increase in the surface area per headgroup of the surfactant as a consequence of an enhanced solvation, probably induced by the incorporation of some glycerol molecules in the micellar solvation layer. Although the pyrene 1:3 ratio index does not indicate significant changes in the micropolarity at the micelle-bulk interface, the data of fluorescence anisotropy of coumarin 6 and fluorescein are compatible with the formation of a more compact solvation layer.     

Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K^1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.     

Micellization of Sodium Dodecyl Sulfate in Glycerol Aqueous Mixtures

The effect of glycerol on both micellar formation and the structural evolution of the sodium dodecyl sulfate (SDS) aggregates in the context of the action mechanism of the cosolvent has been studied. The critical micelle concentration and the degree of counterion dissociation of the surfactant over a temperature range from 20°C to 40°C were obtained by the conductance method. The thermodynamic parameters of micellization were estimated by using the equilibrium model of micelle formation. The analysis of these parameters indicated that the lower aggregation of the surfactant is mainly due to a minor cohesive energy of the mixed solvent system in relation to the pure water. The effect of glycerol on the mean aggregation number of the micelles of SDS was analyzed by the static quenching method. It was found that the aggregation number decreased with the glycerol content. This reduction in the micellar size seems to be controlled by an increase in the surface area per headgroup, which was ascribed to a participation of glycerol in the micellar solvation layer. Studies on the micropolarity of the aggregates, as sensed by the probe pyrene, indicated that this microenvironmental parameter is almost unaffected by the presence of glycerol in the mixture. However, an increase in the micellar microviscosity at the surface region was observed from the photophysical behavior of two different probes, rhodamine B and auramine O. These results suggest a certain interaction of the cosolvent in the micellar solvation of SDS micelles.     

Concentrations of Monomers and Cylindrical Micelles above the Second CMC

Based on thermodynamically substantiated linear dependence of the work of cylindrical micelle formation on the aggregation number within a wide range of aggregation numbers where the cylindrical micelles are accumulated in a surfactant solution, the second critical micellization concentration (CMC) is introduced as an overall surfactant concentration at which the ratio of the total amount of substance in cylindrical micelles to the amount of substance in monomers is equal to 0.1, i.e., it is already noticeable. It is shown that this ratio increases rather rapidly with a monomer concentration. The coefficient of the linear dependence of the work of cylindrical micelle formation on the aggregation number in the important practical situation where the ratios of the total concentration of cylindrical micelles and total amount of substance in these micelles to the monomer concentration are equal by the order of magnitude to 1 and 10⁵, respectively, while disc micelles and extended bilayers are still not appeared. In the same situation, the ratios of the total concentration of spherical micelles and total amount of substance in these micelles to the monomer concentration are equal by the order of magnitude to 1 and 10², respectively. The relationship between the overall surfactant concentration and monomer concentration is found. It is shown that the second CMC exceeds by two orders of magnitude the first CMC corresponding to the onset of the noticeable accumulation of surfactant in spherical micelles. The distribution of cylindrical micelles over the aggregation numbers is analyzed. It is demonstrated that, in agreement with the experiment, the distribution is almost uniform in the considerable part of the wide range of aggregation numbers and drops exponentially in the remaining (right-hand) part of this range. Experimental result is confirmed that the total concentration of cylindrical micelles, the mean value, and the mean statistical scatter of aggregation numbers in a cylindrical micelle is proportional to the square root of the overall surfactant concentration. The balance equation of surfactant amount in the vicinity of the final equilibrium state of a materially isolated solution is linearized. This linearization makes it possible to express the deviations of monomer and aggregate concentrations from their equilibrium values at the lower boundary of the region of the linear dependence of the work of cylindrical micelle formation on the aggregation numbers via the deviations of experimentally observed total concentrations of spherical and cylindrical micelles from their equilibrium values. The case of the solutions of such surfactants, for which spherical shape appeared to be unrealizable due to their molecular structure and packing conditions, is considered separately.     

Micellar solutions of ionic surfactants and their mixtures with nonionic surfactants: Theoretical modeling vs. Experiment

Here, we review two recent theoretical models in the field of ionic surfactant micelles and discuss the comparison of their predictions with experimental data. The first approach is based on the analysis of the stepwise thinning (stratification) of liquid films formed from micellar solutions. From the experimental step-wise dependence of the film thickness on time, it is possible to determine the micelle aggregation number and charge. The second approach is based on a complete system of equations (a generalized phase separation model), which describes the chemical and mechanical equilibrium of ionic micelles, including the effects of electrostatic and non-electrostatic interactions, and counterion binding. The parameters of this model can be determined by fitting a given set of experimental data, for example, the dependence of the critical micellization concentration on the salt concentration. The model is generalized to mixed solutions of ionic and nonionic surfactants. It quantitatively describes the dependencies of the critical micellization concentration on the composition of the surfactant mixture and on the electrolyte concentration, and predicts the concentrations of the monomers that are in equilibrium with the micelles, as well as the solution’s electrolytic conductivity; the micelle composition, aggregation number, ionization degree and surface electric potential. These predictions are in very good agreement with experimental data, including data from stratifying films. The model can find applications for the analysis and quantitative interpretation of the properties of various micellar solutions of ionic surfactants and mixed solutions of ionic and nonionic surfactants.     

Microcalorimetric and conductivity studies with micelles prepared from multi-headed pyridinium surfactants

A set of novel single-chain surfactants bearing one (P1), two (P2), and three (P3) pyridinium headgroups have been synthesized in an attempt to achieve control over the aggregate properties. The critical micellar concentrations (cmc's) and the degrees of counterion dissociation (alpha) of micelles of these surfactants were determined by conductometry. The cmc and the alpha values increased with increase in the number of headgroups of the surfactant. The thermodynamics of micellization of these surfactants were investigated by microcalorimetry, and the results were compared with that of well-known single-chain/single-headgroup surfactant, cetylpyridinium bromide (CPB). The relationship between the cmc of surfactant in solution and its free energy of micellization (deltaG(o)m) was derived for each surfactant. Exothermic enthalpies of micellization (deltaH(o)m) and positive entropies of micellization (deltaS(o)m) were observed for all the surfactants. deltaH(o)m values were found to be more negative for CPB than P1, and it increased with a negative sign from P1 to P2 and decreased for P3. In contrast the deltaS(o)m values decreased with increase in the number of headgroups. The deltaG(o)m values progressively became less negative with increase in the number of headgroups. This implies that micelle formation becomes less favorable as more headgroups are incorporated in the surfactant.